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Priyansh Goel Grade:
        

Find the locus of midpoint of variable chord of parabola y2 = 4ax such  that tangents make an angle Φ between them.

6 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Priyansh


let the mid point is (h,k)


and let the point where tangent touch the parabola is (at12,2at1) and (at22,2at2)


 


so 2h = a(t12 + t22)    and  2k = 2a(t1+t2)   ...................1


 


from equation 1 find the value of t1t2 = (k2 -2ha)/2a2


and |t1-t2| = 1/a {k2 - 4ha}1/2


so given tanΦ = |m1-m2|/(1+m1m2)


where m1 = 1/t1


            m2 =1/t2


 


so put these value


tanΦ =2a{k2 -4ha}1/2 / {k2 -2ha}



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Badiuddin

6 years ago
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